Which of the following three-dimensional figures has five vertices and five faces?
A rectangular pyramid has five vertices and five faces.
A rectangular pyramid consists of a rectangular base and four triangular faces that converge at a single apex, resulting in a total of five vertices and five faces. This unique structure distinguishes it from other three-dimensional figures.
As stated, a rectangular pyramid features one rectangular face at the base and four triangular faces, totaling five faces. Additionally, it has five vertices: four at the base corners and one at the apex. This combination of faces and vertices meets the criteria specified in the question.
A triangular pyramid, also known as a tetrahedron, has four vertices and four faces: three triangular faces forming the sides and one triangular face at the base. This does not satisfy the requirement for five vertices and five faces, making it an incorrect choice.
A rectangular prism has eight vertices and six faces, consisting of three pairs of rectangular faces. The number of vertices and faces does not align with the question's criteria, thereby disqualifying it as a correct answer.
A triangular prism features six vertices and five faces: two triangular faces at the ends and three rectangular faces connecting them. While it has five faces, the total vertex count is six, which does not meet the requirement of five vertices.
In summary, the only three-dimensional figure that meets the criteria of having five vertices and five faces is a rectangular pyramid. Both the triangular pyramid and the rectangular prism do not possess the correct number of vertices or faces, while the triangular prism has too many vertices. This clear distinction highlights the unique geometric properties of the rectangular pyramid.
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